This invention relates to the generation of waveforms which are particularly useful in PWM-driven motors and, more particularly, to the generation of triangle waveforms which are synthesized from a reference n-phase sine wave signal.
In the motor control art, it is conventional to drive an AC motor from an inverter which, typically, is provided with silicon-controlled rectifiers (SCR's) which function as switches that respond to control signals to supply drive currents to the motor. For example, a basic inverter circuit for driving a 3-phase motor is provided with a pair of SCR's for each phase. When one SCR in a particular phase is energized, or turned ON, DC current flows to the corresponding motor phase in a first direction; and when the other SCR in that pair is turned ON, DC current flows to this motor phase in the opposite direction. Control circuits are connected to the inverter so as to energize the respective pairs of SCR's sequentially and in the proper order such that the appropriate motor phases are supplied with positive and negative DC currents in a repetitive manner. Thus, direct current is switched by the inverter so as to drive the 3-phase AC motor.
One type of inverter that has been used advantageously is the so-called pulse width modulated (PWM) inverter. In the PWM inverter, the SCR's are turned ON and OFF in response to pulse width modulated control pulses. As the frequency of these PWM pulses increases, the rate at which the SCR's turn ON and OFF also increases. The duration of each PWM pulse determines the amount of current that is supplied to the motor by the SCR; and this duration may be a function of the amplitude of a reference signal which is used to control the motor.
One type of known PWM generator which has been used to supply PWM signals to the inverter operates by comparing a triangle waveform to a reference signal. A pulse signal is generated in accordance with each intersection of the triangle waveform and reference signal. For example, when the rising edge (i.e. positively sloped edge) crosses the reference signal, the leading edge of the pulse is generated, and when the falling edge (i.e. the negatively sloped edge) crosses the reference signal, the trailing edge of the pulse is generated. The polarity of the pulse, that is, whether the pulse appears as a positive-going or a negative-going pulse, is determined as a function of the polarity of the reference signal.
One technique for generating the triangle waveform is described in U.S. Pat. No. 3,624,486. In this patent, a digital circuit generates a rectangular wave signal of desired frequency, and this rectangular wave signal charges and discharges a capacitor. As the capacitor charges, the positively sloped edge of triangle waveform is produced; and as the capacitor discharges, the negatively sloped edge of the triangle waveform is produced. The frequency of the triangle waveform is equal to the frequency of the rectangular wave signal. Consequently, as the rectangular wave frequency increases, the capacitor does not have sufficient time to charge to a higher level, thereby resulting in a triangle waveform of reduced amplitude. Conversely, as the rectangular wave frequency decreases, the amplitude of the triangle waveform increases. A PWM signal is produced, in accordance with this patent, by comparing the variable amplitude triangle waveform with another rectangular wave reference signal. However, since the pulse duration of the PWM signal is a function of the amplitude of the triangle waveform which, in turn, is dependent upon the frequency of the rectangular wave signal from which the triangle waveform is generated, and also is a function of the amplitude of the rectangular wave reference signal, it is difficult to obtain good control over the PWM signal. For this reason, use of this patent is best restricted to generating a PWM signal of a substantially constant frequency. This means that, if the PWM signal is used to drive an AC motor, this motor must be driven at a substantially constant speed.
It is, of course, desirable to control the speed at which the motor is driven. When a motor is driven at a lower speed, the SCR's included in the inverter are switched at a relatively lower frequency. Conversely, these SCR's are switched at a relatively higher frequency when the motor is driven at a higher speed. There is an upper limit on the frequency at which the SCR's can be driven. Generally, this upper limit is on the order of about 400 Hz. It is advantageous, as described in U.S. Pat. No. 3,916,285, to operate the SCR's in the vicinity of its higher frequency limit for all motor speeds. Thus, for lower speeds, it is necessary that the triangle waveform which is used to generate the PWM pulses exhibit a higher frequency, for example, about three times the frequency of the triangle waveform which is used to generate the PWM pulses at higher motor speeds. The purpose of the higher triangle wave frequency is to increase the order of the harmonic component which would be included in the PWM pulse signal. One difficulty associated with unwanted harmonics of the PWM signal is that harmonic currents flow through the motor, thereby increasing copper losses therein. Such harmonic currents are limited by the leakage inductance of the motor and, as appreciated, the magnitudes of these currents are inversely related to their harmonic frequencies. That is, if the harmonic frequency of the current is high, the magnitude of that current is maintained at a lower amplitude.
It has been proposed, in U.S. Pat. No. 4,047,083, to use a sine wave signal as the reference signal to which the triangle waveform is compared for producing the PWM inverter drive pulses. Motor speed control is attained by controlling the frequency and amplitude of this sine wave reference signal. According to this patent, it is desirable that a relatively high "chopping ratio" be maintained. The chopping ratio is the ratio of the frequency of the triangle waveform to the frequency of the sine wave signal. With a high chopping ratio, that is, a chopping ratio that is greater than six, the residual harmonics in the PWM signal have a high order and, thus, little influence on motor operation. Harmonic distortion in the output voltage waveform is relatively low.
This patent also recognizes the problem of low frequency "beats" due to unwanted subharmonic components. These subharmonic components may be present if the triangle waveform is not precisely synchronized with the sine wave signal. For example, if the triangle wave frequency is 301 Hz and the sine wave frequency is 50 Hz, then the sixth harmonic of the sine wave frequency (i.e. 300 Hz) will interfere with the triangle wave frequency of 301 Hz resulting in a beat component of 1 Hz. Although this problem is minimized with proper synchronism between the triangle waveform and sine wave signal, this patent points out that it is extremely difficult to obtain such synchronism. The problem of synchronizing the triangle waveform and sine wave signal is avoided by setting the triangle wave frequency at six times the sine wave frequency (i.e. providing a chopping ratio of six), thereby limiting the operation of the motor to a relatively low range of speeds.
One disadvantage of the aforenoted motor-drive circuit is that motor speed control is constrained to a relatively low range of speeds. As the sine wave frequency increases, the triangle wave frequency (which is not synchronized with the sine wave frequency) likewise must be increased, while maintaining the chopping ratio of six. Consequently, the frequency of the PWM pulses soon will reach the limit at which the SCR's in the inverter can be switched.
In accordance with one advantageous feature of the present invention, to be described in detail, the triangle waveform is synthesized from the sine wave signal such that the triangle wave frequency automatically is in precise synchronism with the sine wave frequency. The triangle waveform naturally includes a gradually increasing (or positively sloped) edge and a gradually decreasing (or negatively sloped) edge. These edges are substantially linear such that proper PWM pulses are generated in accordance with the intersection of the triangle waveform and the sine wave signal.
Another advantageous feature of the present invention is the ability to control motor speed over a relatively wide range. To avoid deleterious influences attributed to higher order harmonics, the chopping ratio is changed over when the sine wave frequency reaches different discrete values. For example, at relatively lower motor speeds, the chopping ratio is selected to be equal to 9. The motor speed is increased as the sine wave frequency increases, and when this sine wave frequency reaches, for example, 38 Hz, the chopping ratio is reduced to six. As the motor is further increased by increasing the sine wave frequency, the chopping ratio is changed over to three at a sine wave frequency of, for example 50 Hz. The higher order triangle wave frequencies are produced by a novel amplitude folding technique in accordance with one aspect of the present invention. That is, by operating on the fundamental triangle waveform, the higher order triangle waveforms are generated, these higher order waveforms being exactly synchronized with the sine wave signal and also with the fundamental triangle waveform. A desirable feature of this amplitude folding technique is that the zero crossings of the higher order triangle waveforms coincide with the zero crossing of the fundamental triangle waveform. Consequently, transition disturbances are not introduced when changing over from higher order to lower order (or vice versa) triangle waveforms to produce the PWM pulses.
A sawtooth waveform generator wherein the sawtooth signal is synthesized from four phases of a sine wave signal is described in U.S. Pat. No. 2,580,673. In this generator, two of the four sine wave phases are shifted in amplitude, and then a segment of each phase, taken at 45.degree. on either side of the zero axis of that phase, is selected. This results in a non-linear sloping side and an abrupt return to a base or reference level at the end of each sawtooth so as to commence the next following sawtooth. The resultant sawtooth waveform is totally undesirable for use in a PWM generator. This is because the sawtooth waveform includes only gradually rising (or gradually falling) edges. Each sawtooth wave begins and ends on a vertical edge. If these vertical edges are used to generate PWM pulses to drive a three-phase motor, the line voltage across the motor at each vertical edge will have no effect. That is, one-half of all commutations would be wasted. As a consequence thereof, the harmonic content in the drive pulses supplied to the motor would seriously degrade the operation thereof.